{"paper":{"title":"Formal conserved quantities for isothermic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"F. E. Burstall, S. D. Santos","submitted_at":"2013-01-03T13:18:51Z","abstract_excerpt":"Isothermic surfaces in $S^n$ are characterised by the existence of a pencil $\\nabla^t$ of flat connections. Such a surface is special of type $d$ if there is a family $p(t)$ of $\\nabla^t$-parallel sections whose dependence on the spectral parameter $t$ is polynomial of degree $d$. We prove that any isothermic surface admits a family of $\\nabla^t$-parallel sections which is a formal Laurent series in $t$. As an application, we give conformally invariant conditions for an isothermic surface in $S^3$ to be special."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0447","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}